Detecting responses of micro-electromechanical system (mems) resonator device

ABSTRACT

A system for detecting responses of a MEMS resonator device includes first and second signal sources, a signal divider and a frequency mixer. The first signal source provides a first signal and the second signal source provides a second signal that electrostatically drives the MEMS resonator device, causing mechanical vibration. The signal divider divides the first signal into a probe signal and a local oscillator (LO) signal, the probe signal being applied to the MEMS resonator device and reflected by a capacitance of the MEMS resonator device. A reflection coefficient is modulated onto the reflected probe signal at the mechanical resonance frequency by variations in the capacitance induced by the mechanical vibration of the MEMS resonator device. The frequency mixer mixes the reflected probe signal and the LO signal and outputs an intermediate frequency (IF) signal, which represents modulation of the reflection coefficient, providing an image of the mechanical vibration.

BACKGROUND

There are various types of miniaturized micro-electromechanical systems(MEMS) devices, including MEMS resonator devices, which transposeproperties of mechanical resonance in the electrical domain. Potentialapplications of MEMS resonator devices include electrical signalprocessing (e.g. filtering, providing time references, etc.) andvibrating sensors (e.g., inertial sensors, mass detectors, label freedetectors, pressure sensors, force sensors, etc.), for example. MEMSresonator devices used as vibrating sensors may be incorporated intoatomic force microscopy(AFM) applications.

Various physical principles may be used to assure electromechanicaltransduction performed by the MEMS resonator devices. For example,capacitive transducers are widely employed because they are easilyintegrated with the mechanical part, and have well establishedfabrication processes compatible with semiconductor integrated circuittechnologies. However, capacitive transducers generally have twodrawbacks, as transducers are downsized to reach higher resonancefrequencies. First, capacitive transducers present electrical impedancethat significantly exceeds the 50-ohm standard. Second, capacitivetransducers have parasitic input/output coupling capacitance. Therefore,the measured signal from a capacitive transducer is generally weak andsuperimposed on a parasitic signal floor, which may mask the desiredmechanical resonance signal. The high impedance value (e.g., severalkilo-ohm) presented by the MEMS resonator devices to the measurementset-up, typically a vector network analyzer, negates much of the benefitthat would be otherwise attained from optimal sensitivity andmeasurement dynamic. Therefore, electrical characterizations of the MEMSresonator devices exhibit particularly poor signal-to-noise ratios.

SUMMARY

In a representative embodiment, a system for detecting responses of amicro-electro mechanical system (MEMS) resonator device includes firstand second signal sources, a signal divider and a frequency mixer. Thefirst signal source is configured to provide a first signal having afirst frequency. The second signal source is configured to provide asecond signal having a second frequency, the second signalelectrostatically driving the MEMS resonator device at about amechanical resonance frequency, causing mechanical vibration of the MEMSresonator device. The signal divider is configured to divide the firstsignal into a probe signal and a local oscillator (LO) signal, the probesignal being applied to the MEMS resonator device and reflected by acapacitance of the MEMS resonator device to provide a reflected probesignal where a reflection coefficient is modulated onto the reflectedprobe signal at the mechanical resonance frequency by variations in thecapacitance induced by the mechanical vibration of the MEMS resonatordevice. The frequency mixer is configured to mix the reflected probesignal and the LO signal and to output an intermediate frequency (IF)signal, the IF signal representing modulation of the reflectioncoefficient, providing an image of the mechanical vibration of the MEMSresonator device.

In another representative embodiment, a system for detecting microscopicparticles in anatomic force microscopy (AFM) application includes firstand second signal sources, and a mixer. The first signal source isconfigured to provide a probe signal to a MEMS resonator device via afirst signal path, the probe signal being reflected by a capacitance ofthe MEMS resonator device to provide a reflected probe signal modulatedby a reflection coefficient. The second signal source is configured toprovide a stimulus signal to the MEMS resonator device via a secondsignal path, the stimulus signal electrostatically driving the MEMSresonator device at about a mechanical resonance frequency, causingmechanical vibration of the MEMS resonator device, where the reflectioncoefficient is modulated on the reflected probe signal by variations inthe capacitance induced by the mechanical vibration of the MEMSresonator device. The mixer configured to mix the reflected probe signaland an LO signal, having an LO frequency equal to a frequency of theprobe signal, to demodulate the reflected probe signal and to output anIF signal, where the IF signal includes the reflection coefficient forproviding an image of the mechanical vibration of the MEMS resonatordevice.

In another representative embodiment, a method is provided for detectingresponses of a MEMS resonator device. The method includes applying astimulus signal to a first transducer of the MEMS resonator device toinduce mechanical vibration; applying a probe signal to a secondtransducer of the MEMS resonator device; receiving a reflected probesignal from the second transducer of the MEMS resonator device, thereflected probe signal having a reflection coefficient modulated ontothe reflected probe signal at a resonance frequency of the MEMSresonator device by variations in a capacitance of the second transducerinduced by the mechanical vibration of the MEMS resonator device; anddemodulating the reflected probe signal with an LO signal to obtain anIF signal, providing an image of mechanical vibration, the LO signalhaving the same frequency as the probe signal.

BRIEF DESCRIPTION OF THE DRAWINGS

The illustrative embodiments are best understood from the followingdetailed description when read with the accompanying drawing figures. Itis emphasized that the various features are not necessarily drawn toscale. In fact, the dimensions may be arbitrarily increased or decreasedfor clarity of discussion. Wherever applicable and practical, likereference numerals refer to like elements.

FIG. 1 is a block diagram illustrating a system for providing microwavemeasurement of a micro-electro mechanical systems (MEMS) resonatordevice, according to a representative embodiment.

FIG. 2 is a top plan view of an illustrative MEMS resonator device ofFIG. 1.

FIG. 3 includes traces showing frequency response of a MEMS resonatordevice driven by the microwave measurement system of FIG. 1, accordingto a representative embodiment.

FIG. 4 includes traces showing performance of a MEMS resonator device(signal-to-noise ratio) driven by the microwave measurement system ofFIG. 1, according to a representative embodiment.

FIG. 5 includes traces showing S-parameter measurements and frequencyresponse of a MEMS resonator device driven by the microwave measurementsystem of FIG. 1, according to a representative embodiment.

FIG. 6 is a flow diagram depicting a method for detecting responses of aMEMS resonator device, according to a representative embodiment.

DETAILED DESCRIPTION

In the following detailed description, tor purposes of explanation andnot limitation, illustrative embodiments disclosing specific details areset forth in order to provide a thorough understanding of embodimentsaccording to the present teachings. However, it will be apparent to onehaving had the benefit of the present disclosure that other embodimentsaccording to the present teachings that depart from the specific detailsdisclosed herein remain within the scope of the appended claims.Moreover, descriptions of well-known devices and methods may be omittedso as not to obscure the description of the example embodiments. Suchmethods and devices are within the scope of the present teachings.

Generally, it is understood that the drawings and the various elementsdepicted therein are not drawn to scale. Further, relative terms, suchas “above,” “below,” “top,” “bottom,” “upper,” “lower,” “left,” “right,”“vertical” and “horizontal,” are used to describe the various elements'relationships to one another, as illustrated in the accompanyingdrawings. It is understood that these relative terms are intended toencompass different orientations of the device and/or elements inaddition to the orientation depicted in the drawings. For example, ifthe device were inverted with respect to the view in the drawings, anelement described as “above” another element, for example, would now be“below” that element. Likewise, if the device were rotated 90 degreeswith respect to the view in the drawings, an element described as“vertical,” for example, would now be “horizontal.”

Generally, various representative embodiments provide systems andmethods for detecting responses of a micro-electro mechanical system(MEMS) resonator device. The embodiments circumvent previous limitationsand provide electromechanical measurements of MEMS resonator devicesfeaturing excellent signal-to-noise ratio and large rejection ofparasitic capacitive coupling signals.

FIG. 1 is a block diagram illustrating a system for providing microwavemeasurement of a micro-electromechanical systems (MEMS) resonatordevice, according to a representative embodiment.

Referring to FIG. 1, measurement system 100 includes MEMS resonatordevice 110, which may be referred to as a device under test (DUT). In anembodiment, the measurement system 100 may be used in an AFMapplication, for example, where the MEMS resonator device 110 acts as avibrating sensor. That is, microscopic particles attach to a vibratingportion of the MEMS resonator device 110 (e.g., ring resonator 115,discussed below), which alters the frequency of mechanical resonance andthe frequency response transfer function. An example of a MEMS resonatordevice is described by Faucher et al. in U.S. Patent ApplicationPublication Number 2010/0205698, entitled “Atomic Force MicroscopyProbe” (Aug. 12, 2010), which is hereby incorporated by reference. Thealteration in the frequency is detected, e.g., by receiver 160,indicating the presence and/or type of microscopic particles.

In the depicted embodiment, the MEMS resonator device 110 has two ports.A first port is connected to a first signal source 120 via a firstsignal path and the second port is connected to a second signal source130 via a second signal path, where the first signal source 120 providesfirst signal S1 and the second signal source 130 provides second signalS2. Generally, the first signal path includes (optional) circulator 128,high-pass filter 129 and (optional) first bias-tee 125, and the secondsignal path includes second bias-tee 135 and low-pass filter 139,details of which are discussed below.

FIG. 2 is a top plan view of an illustrative MEMS resonator device thatmay be incorporated as the MEMS resonator device 110 of FIG. 1,according to a representative embodiment. Of course, other types of MEMSresonator devices, with or without ring oscillators, may be incorporatedwithout departing from the scope of the present teachings. Referring toFIG. 2, the MEMS resonator device 110 includes a ring resonator 115suspended in cavity 114 by four connectors 116, which may be membranes,for example, arranged at substantially equal intervals around the outerperimeter of the ring resonator 115. The cavity 114 is formed insubstrate 113. The MEMS resonator device 110 further includes a scanningprobe microscopy (SPM) tip or probe tip 119, which contacts a surface ofsample 170, causing changes in the mechanical movement or vibration ofthe ring resonator 115. The general direction of the mechanical movementis indicated by an arrow. It is understood that the MEMS resonatordevice 110 may include types of resonators other than representativering resonator 115, such as a thin piezoelectric layer resonator, invarious configurations, without departing from the scope of the presentteachings.

The MEMS resonator device 110 further includes electromechanicalcapacitive transducers, shown as first (input) capacitive transducer 111and second (output) capacitive transducer 112. The first capacitivetransducer 111 is separated from an outer perimeter of the ringresonator 115 by first capacitive air gap 111 a, and the secondcapacitive transducer 112 is separated from the outer perimeter of thering resonator 115 by second capacitive air gap 112 a on an oppositeside of the ring resonator 115 from the first capacitive air gap 111 a.The first capacitive transducer 111 is used to drive the MEMS resonatordevice 110 close to its resonance frequency, causing correspondingvibration of ring resonator 115. The second capacitive transducer 112 isused to sense mechanical displacements of the ring resonator 115. Tirefirst and second capacitive transducers 111 and 112 receive and sendelectrical signal signals (e.g., second signal S2, probe signal PS andreflected probe signal RPS, discussed below) via conductors 117 and 118,respectively.

The substrate 113 may be formed of any appropriate substrate material,such as silicon (Si), gallium arsenide (GaAs), indium phosphide (InP),glass, or the like. The ring resonator 115 and the connectors 116 may beformed of any material that provides mechanical vibration in response toa stimulus signal (e.g., second signal S2), such as Si or Si basedmaterial (doped for conductivity), GaAs or InP, for example. Theconductors 117 and 118 are formed of any appropriate conductivematerial, such as gold (Au), copper (Cu), aluminum (Al), or the like.

Referring again to FIG. 1, the first signal S1 provided by the firstsignal source 120 is a microwave signal having a first frequency in therange of about 1 GHz to about 50 GHz, for example. The available powerof the first signal source 120 is divided into two parts by signaldivider 140, providing the probe signal PS to the first signal path anda local oscillator (LO) signal LOS provided to a LO signal path,discussed below. The first signal 81, the probe signal PS and the LOsignal LOS have the same frequency (i.e., the first frequency). Thesignal divider 140 may be a directive coupler or a resistive divider,for example, connected to ground via resistor 141.

The second signal S2 provided by the second signal source 130 is a radiofrequency (RF) signal having a second frequency in the range of about 1MHz to about 300 MHz, for example. The second frequency is selected sothat the second signal S2 electrostatically drives the MEMS resonatordevice 110 at about its mechanical resonance frequency, causingmechanical vibration of the ring resonator 115 in the MEMS resonatordevice 110.

More particularly, the second signal source 130 provides the secondsignal S2 to the second signal path, which includes the second bias-tee135 and the low-pass filter 139. The second bias-tee 135 includescapacitor 136, connected in series between the second signal source 130and the low-pass filter 139, and inductor 137, connected between secondauxiliary input/output 132 and the capacitor 136. The second bias-tee135 applies DC bias from the second auxiliary input/output 132 to thesecond signal 82 to produce an electrostatic driving force, inconjunction with the second signal source 130 in MHz frequencies and DC,input to the MEMS resonator device 110. The low-pass filter 139 providesisolation from higher frequencies existing in other parts of themeasurement system 100. The cut-off frequency of the low-pass filter 139is greater than the highest frequency generated by the second signalsource 130.

As mentioned above, the first signal S1 is divided into the probe signalPS and the LO signal LOS by the signal divider 140, each of which hasthe microwave carrier frequency of the first signal S1. The probe signalPS is used to sense the mechanical vibration of the MEMS resonatordevice 110. The probe signal PS is applied to the MEMS resonator device110 through the circulator 128, the high-pass filter 129 and the(optional) first bias-tee 125 of the first signal path. In variousconfigurations, other types of isolating components, such as a coupler,may be used in place of the circulator 128. The high-pass filter 129provides isolation from higher frequencies existing in other parts ofthe measurement system 100, as well as reduces leakage of the secondsignal source 130 back to the circulator 128, keeping frequency mixer(“mixer”) 150 in linear operation and out of saturation. The cut-offfrequency of the high-pass filter 129 is greater than the cut-offfrequency of the low-pass filter 139 and lower than the first frequencyof the first signal S1 generated by the first signal source 120.

The first bias-tee 125 includes capacitor 126, connected in seriesbetween the high-pass filter 129 and the MEMS resonator device 110, andinductor 127, connected between first auxiliary input/output port 122and the capacitor 126. The first bias-tee 125 applies DC bias from thefirst auxiliary input/output port 122 to the probe signal PS. That is,the first auxiliary input/output port 122 enables DC bias to besuperimposed onto the probe signal PS through first bias-tee 125. Thefirst auxiliary input/output port 122 further enables extraction of anylow frequency signal output by the MEMS resonator device 110 foranalysis. For example, reflection and transmission parameters of MEMSresonator device 110 may be measured via the first auxiliaryinput/output port 122 at the frequency of the second signal S2 from thesecond signal source 130 (i.e., the resonance frequency of the MEMSresonator device 110). Changes in mechanical resonance parameters of theMEMS resonator device 110 driven by the second signal source 130 causedby external influences (e.g., interaction of the probe tip 119 and thesurface of the sample 170) are superimposed onto the frequency of thereflected probe signal RPS. In other words, the frequency responsetransfer function of the MEMS resonator device 110 is modulated onreflected probe signal (RPS) and demodulated via the mixer 150,discussed below, such that measurements may be performed by the receiver160, for example, or other measuring instrument.

In the depicted embodiment, the probe signal PS is reflected by thesecond capacitive transducer 112 of the MEMS resonator device 110,providing the reflected probe signal RPS. The corresponding reflectioncoefficient of the reflected probe signal RPS is modulated by variationsin capacitance of the second capacitive transducer 112. These variationsin the capacitance are induced by the mechanical vibration of the ringresonator 115 in the MEMS resonator device 110, resulting fromapplication of the second signal S2 (stimulus signal), as discussedabove. The reflected probe signal RPS travels through the first bias-tee125 and the high-pass filter 129, and is separated from the incidentprobe signal PS by the circulator 128. The separated reflected probesignal RPS is then applied to an RF input port of the mixer 150. It isunderstood that addition electrical components, such as attenuatorsand/or amplifiers, may be included in the first signal path of the probesignal PS and the reflected, probe signal RPS to adjust the respectivepower levels, as would, be apparent to one of ordinary skill in the art.

Meanwhile, as mentioned, above, the LO signal LOS output by the signaldivider 140 is provided to the LO signal path, which includes (optional)circulator 142, phase shifter 144 and band-pass filter 146. Thecirculator 142 is used as an isolator, and may be connected to groundvia resistor 143. In various configurations, other types of components,such as an amplifier, may be used in place of the circulator 142. Thephase shifter 144 adjusts a delay of the LO signal LOS, and theband-pass filter 146 filters the LO signal LOS to remove added noise andspurious signals. The center frequency of the band-pass filter 146 issubstantially the same as the center frequency of the first signal S1,provided by the first signal source 120. The LO signal LOS output fromthe band-pass filter 146 of the LO signal path is applied to the LOinput port of the mixer 150. It is understood that additional electricalcomponents, such as attenuators and/or amplifiers, may be included inthe LO signal path to adjust the powrer level, e.g., depending on therequirements of the mixer 150, as would be apparent to one ofordinaryskill in the art. The phase adjustment of the LO signal LOS by the phaseshifter 144 optimizes operation of the mixer 150, wrhich may operate asa homodyne downconverter, for example.

Intermediate frequency (IF) signal IFS is available at an IF output portof the mixer 150. The IF signal IFS represents the modulation of thereflected probe signal RPS provided to the RF input port of the mixer150. Thus, the IF signal IFS represents the modulation of the reflectioncoefficient of the reflected probe signal RPS, described above, andprovides an image of the mechanical vibration of the MEMS resonatordevice 110. As mentioned above, the phase shifter 144 adjusts the delayof the LO signal LOS to insure that the LO signal LOS, input to an LOinput port of the mixer 150, and the reflected portion of reflectedprobe signal RPS that is caused by the changes of the capacitance of thering resonator 115 at equilibrium (refer to Equation (1) below) input tothe RF input port of the mixer 150, are in phase (or 180 degrees out ofphase) for optimum performance. Also, since the main part of thereflected probe signal RPS that is caused by the ring resonatorcapacitance at equilibrium and the portion that is caused by changes ofthe capacitance from equilibrium are orthogonal (90 degree out ofphase), the portion output by the mixer 150 that corresponds to mainpart of reflection will be zero (or highly attenuated), since the LOsignal LOS and the main part of the reflected probe signal RPS are 90degrees out of phase and a homodyne mixer is used as a down converter.

Also, the main portion of the reflected probe signal RPS has far greateramplitude than the portion of the reflected probe signal RPS signalcaused by the changes of the capacitance of the ring resonator 115 fromequilibrium. Attenuating the main portion of reflected probe signal RPSthrough the homodyne mixer helps to elevate the possibility ofoverdriving IF signal processing components. Also, phase noise of thereflected probe signal RPS will be down converted to the IF signal IFSvia the LO signal LOS (90 degree phase shift between the two signals),which may degrade the signal to noise ratio of the measurement.Therefore a signal with low phase noise should be used as a drivingsignal. Since the MEMS resonator operates at tens of MHZ, a source withlow phase noise at tens of MHZ away from the carrier is easily obtained,commercially.

The IF signal IFS is provided to the receiver 160 via an IF signal path,which includes block capacitor 152, first amplifier 154, low-pass filter156 and second amplifier 158 (optional). The block capacitor 152suppresses the DC component of the IF signal IFS. The IF signal IFS isthen amplified by the first amplifier 154, which may be a low-noiseamplifier, for example. The low-pass filter 156 eliminates undesirablehigh frequencies components. The second amplifier 158 may also beincluded in the IF signal path for additional amplification of the IFsignal IFS.

The amplified IF signal IFS is provided to an input port of the receiver160, for example, to be analyzed in terms of magnitude and phase. Themagnitude and phase of the IF signal IFS as compared to the secondsignal S2 represents dynamic change in the MEMS resonator device 110.For example, the MEMS resonator device 110 with probe tip 119 may beused for AFM imaging to measure mechanical properties of the surface ofthe sample 170, such as topography, elasticity and the like. This can beachieved via comparison of the IF signal IFS and the second signal S2 asa reference. Also, the IF signal IFS may be used to measure any otherchanges, such as biological binding, which change the weight at the endof the probe tip 119 and therefore change the mechanical resonance ofthe MEMS resonator device 110. For an AC or tapping mode AFM, themagnitude and phase of the fundamental and harmonics of the IF signalIFS may be analyzed with respect to the second signal S2 as a reference,e.g., to determine surface properties of the material being imaged. Suchanalysis would be apparent to the one of ordinary skill in the artregarding AC or tapping mode AFM imaging.

Examples of the receiver 160 include a lock-in amplifier, a spectrumanalyzer, a vector network analyzer, and the like. For example, thereceiver 160 may be a PNA-X Series Nonlinear Vector Network Analyzer(NVNA), available from Agilent Technologies, Inc., or other large-signalnetwork analyzer. In an embodiment, the second signal source 130 may becombined with the receiver 160, e.g., in the NVNA, or may be an RFsignal generator, available from Agilent Technologies, Inc. The firstsignal source 120 may be a microwave synthetizer, such as an E6432A VXIMicrowave Synthesizer, also available from Agilent Technologies, Inc.

Measurement sensitivity of the measurement system 100 is calculated fromthe reflection coefficient of the reflected probe signal RPS, which issensed in the plane of the second capacitive transducer 112 of MEMSresonator device 110, as discussed above. For example, the reflectioncoefficient of the reflected probe signal may be provided by Equation(1), below:

$\begin{matrix}{{\rho (x)} = {\rho_{0}\left\lbrack {1 + {\frac{2\omega \; Z_{C}}{1 + {C^{2}\omega^{2}Z_{C}^{2}}}^{{- {j\pi}}/2}{dC}}} \right\rbrack}} & {{Equation}\mspace{14mu} (1)}\end{matrix}$

Referring to Equation (1), ρ(χ) is the reflection coefficient bringingabout the reflected probe signal RPS in the plane of the secondcapacitive transducer 112 as a function of displacement χ of thevibrating ring resonator 115. The reflection coefficient as indicated byEquation (1) has two main parts, where ρ₀ is the main part of thereflection and is caused by the capacitor in equilibrium. The secondcomponent of the reflection corresponds to the change in the reflectioncoefficient with small mechanical displacement χ caused by the ringresonator vibration. The portion of the reflected probe signal RPS thatis caused by the changes of the capacitance at equilibrium is phaseshifted by −90 degrees from the main portion of the reflected probesignal RPS, which is given by exp(−jπ/2). C is the capacitor value ofthe second capacitive transducer 112 at equilibrium, dC is the variationof the capacitor value when the vibrating ring resonator 115 of the MEMSresonator device 110 moves from its equilibrium position by an amount χ,Z_(C) is the characteristic impedance (e.g., 50Ω), and ω is thepulsation of the probe signal PS provided by the first signal source120.

Assuming that the mechanical displacement χ is small, the capacitorvariation dC can be considered as proportional to the mechanicaldisplacement χ, in which case the information related to the vibrationis in quadrature with respect to the main part of the reflectioncoefficient. The main part of the reflection coefficient is thecapacitance when the vibrating ring resonator 115 is at its equilibrium.As mentioned above, ρ₀ is the reflection coefficient at equilibrium. Thequadrature for the snail mechanical displacement χ comes from exp(−jπ/2)with respect to ρ₀. The measurement sensitivity of the measurementsystem 100 to the capacitor variation dC may thus be given by S inEquation (2):

$\begin{matrix}{S = \frac{2\omega \; Z_{C}}{1 + {C^{2}\omega^{2}Z_{C}^{2}}}} & {{Equation}\mspace{14mu} (2)}\end{matrix}$

In Equation (2), the measurement sensitivity S is at its maximum whenω=1/Z_(C)C, in which case S_(max)=1/C. Further calculations taking intoaccount the signal noise show that measurement resolution up to thezepto-Farad can be achieved in practical cases, where Z_(C) ischaracteristic impedance, e.g., 50 Ohm, and ω is the angular frequencyof the first signal S1.

An illustrative, non-limiting configuration of the measurement system100 was assembled for observing various characteristics, according to arepresentative embodiment In the illustrative configuration, the ringresonator 115 of the MEMS resonator device 110 was a silicon ringresonator having a ring diameter of 60 μm, a thickness of 5 μm, and acalculated resonance frequency is about 25 MHz. The first and secondcapacitive transducers 111 and 112 located along portions of the outerperimeter of the ring resonator 115 formed first and second capacitiveair gaps 111 a and 112 a of about 100 nm, each.

The first signal source 120 generated the first signal S1 having afrequency of about 4 GHz at a power of about 13 dBm. The signal divider140 directed about 3 dBm of the power to the probe signal PS, and about10 dBm of the power to the LO signal LOS. The second signal source 130generated the second signal S2 having a frequency of about 25 MHz forstimulating the ring resonator 115 of the MEMS resonator device 110. Thepower of the second signal source 130 was adjustable, and a 10 V DC biaswas applied to the second signal S2 via second auxiliary input/output132 and the second bias-tee 135.

The first and second amplifiers 154 and 158 each featured about 20 dBgain in the 20 MHz to 30 MHz frequency band and 3 dB noise figure. Thefirst auxiliary input/output port 122 was connected to a receiver of amultiport vector analyzer, in order to measure simultaneously the“classical” S21 transmission parameter of the MEMS resonator device 110.If one replaces the second signal source 130 with the first port of avector network analyzer (VNA), and connects the second port of the VNAto the input port of the first bias-tee 125 in place of the high-passfilter 129, one can characterize the parameters of the MEMS resonatordevice 110 at an RF frequency (here is ˜25 MHz). These results are shownin traces 502 and 503 of FIG. 5, below. In the case of the RFmeasurement, the MEMS transmission measurement at RF shows a great dealof loss, and therefore very low sensitivity. The phase shifter 144 wastuned to adjust the phase of the LO signal LO, and to maximize the IFsignal IFS output by the mixer 150 and received by the receiver 160. TheLO signal LOS and reflected probe signal RPS at the mixer 150 should beinphase or 180 degrees out of phase for optimum performance.

FIG. 3 includes traces showing frequency response of a MEMS resonatordevice 110 driven by the microwave measurement system of FIG. 1,according to a representative embodiment, configured as described above,where fres is the resonance frequency of the MEMS resonator device 110(25.066 MHz), Vdc is the DC bias voltage applied at the second bias-tee135 (10V), P_(drive) is the power of the second signal S2, and IF BW isthe measurement bandwidth of the IF signal IFS output by the mixer 150.Trace 301 shows the phase characterization of the MEMS resonator device110, where the phase shift of the IF signal IFS from 90 degrees to −90degrees occurs at the resonance frequency 25.066 MHz of the MEMSresonator device 110. Generally, as discussed above, the MEMS resonatordevice 110 is driven by the second signal 82 from the second signalsource 130, having an RF frequency of about 25 MHZ. The first signal 81from the first signal source 120 is split into two paths, providing theLO signal LOS and the probe signal PS, respectively. The LO signal LOSis amplified and phase shifted, and the probe signal PS is applied tothe MEMS resonator device 110 as an incident microwave signal. Theincident microwave signal encounters the capacitive load impedance ofthe MEMS resonator device 110, and is reflected as the reflected probesignal RPS. This capacitance changes about the equilibrium capacitanceof the MEMS resonator device 110 due to the ring vibration at the rateof the MEMS resonance frequency, resulting in dC (givenby Equation (2)),which is the deviation from the equilibrium capacitance. The reflectedprobe signal RPS, modulated at the same frequency as the second signalS2, is ultimately mixed by the mixer 150 with the LO signal LOS, whichhas the same carrier frequency as the reflected probe signal RPS. Themixer 150 thus demodulates the reflected probe signal RPS to provide theIF signal IPS, which is delivered to the receiver 160. The IF signal IFSis shown as trace 302 of FIG. 3 (and trace 501 of FIG. 5). Moreparticularly, trace 302 shows the magnitude characterization of the MEMSresonator device 110, which peaks at about 27 dBm at the resonancefrequency 25.066 MHz.

FIG. 4 includes traces showing measurement dynamics of a MEMS resonatordevice 110 driven by the microwave measurement system of FIG. 1,according to a representative embodiment, configured as described above.In particular, FIG. 4 shows traces 401-411 corresponding to frequencyresponses of the MEMS resonator device 110 at different drive powersP_(drive) of the second signal S2, beginning at −90 dBm and separated by10 dBm. In other words, traces 401-411 show the frequency responses ofthe MEMS resonator device 110 at drive power P_(drive)=−90 dBm, −80 dBm,−70 dBm, −60 dBm, −50 dBm, −40 dBm, −30 dBm, −20 dBm, −10 dBm, 0 dBm and10 dBm, respectively. As shown in FIG. 4, the measurement dynamic of theillustrate MEMS resonator device 110 is greater than 100 dB. Thiscorresponds to more than five orders of magnitude for the measurement ofthe resonator vibration amplitude of the MEMS resonator device 110.

The measurement system 100 provides the ability to measure minutechanges the capacitance of the MEMS resonator device 110 from itsequilibrium condition (i.e., the resonator vibrating in air). Forexample, in an illustrative embodiment, as the ring resonator 115 inconjunction with the integrated probe tip 119 approaches a surface ofthe sample 170, just before the probe tip 119 touches the surface itexperiences molecular Van der Waals force, effecting the ring resonator115 excretion by approximately 0.1 Å (Angstrom), which translates tochanges in the dynamic capacitance of the MEMS resonator device 110 bysub-atto Farad. The RF measurement is not capable of sensing such aminute changes due to poor SNR, while the measurement system 100 is ableto perform such measurement.

FIG. 5 includes traces showing S-parameter measurements and frequencyresponse of a MEMS resonator device 110 driven by the microwavemeasurement system of FIG. 1, according to a representative embodiment,configured as described above. In particular, trace 501 of FIG. 5 showsthe measured magnitude characterization of the frequency response of theMEMS resonator device 110. The magnitude characterization peaks at about27 dBm at the resonance frequency 25.066 MHz, as discussed above inregard to FIG. 3. Traces 502 and 503 show classical S-parametermeasurements of transmission (S₂₁) and reflection (S₁₁) of the MEMSresonator device 110 (e.g., taken from first auxiliary input/output port122) under the same driving conditions. Upon comparison, trace 501 showsimproved signal-to-noise ratio, as well as complete suppression ofparasitic coupling signals. That is, comparing trace 501 to 502, one canreadily determine the increase sensitivity when RF stimulus (e.g.,second signal S2) is used. One can use a locking amplifier, for example,to compare the IF signal IFS and second signal S2 to gain insight intonano scale topography.

FIG. 6 is a flow diagram depicting a method for detecting responses of aMEMS resonator device, according to a representative embodiment.

Referring to FIGS. 1, 2 and 6, a stimulus signal (e.g., second signalS2) is applied to the first capacitive transducer 111 of the MEMSresonator device 110 in block S610 to induce mechanical vibration of theMEMS resonator device 110. The frequency of the stimulus signal isselected so that the MEMS resonator device 110 is electrostaticallydriven about its mechanical resonance frequency, causing mechanicalvibration of the ring resonator 115. The stimulus signal may be providedby an RF signal source (e.g., second signal source 130).

In block S620, a probe signal (e.g., probe signal PS) is applied to thesecond capacitive transducer 112 of the MEMS resonator device. Inresponse, a reflected probe signal (e.g., reflected probe signal RPS) isreceived from the second capacitive transducer 112 of the MEMS resonatordevice 110 in block S630. The reflected probe signal has a reflectioncoefficient modulated by variations in a capacitance of the secondcapacitive transducer 112, where the variations in the capacitance areinduced by the mechanical vibration of the MEMS resonator device 110.

The reflected probe signal is mixed with a local oscillator (LO) signal(e.g., LO signal LOS) in block S640 to obtain an intermediate frequency(IF) signal (e.g., IF signal IFS). As discussed above, the IF signalprovides an image of mechanical vibration of the MEMS resonator device110. The LO signal has the same frequency as the probe signal. In anembodiment, the LO signal and the probe signal may be obtained bydividing a microwave signal provided by the same signal source (e.g.,first signal source 120). In block S650, the characteristics of the MEMSresonator device 110 are determined using the IF signal, for example, bythe receiver 160.

While specific embodiments are disclosed herein, many variations arepossible, which remain within the concept and scope of the invention.Such variations would become clear after inspection of thespecification, drawings and claims herein. The invention therefore isnot to be restricted, except within the scope of the appended claims.

What is claimed is:
 1. A system for detecting responses of a micro-electromechanical system (MEMS) resonator device, the system comprising: a first signal source configured to provide a first signal having a first frequency; a second signal source configured to provide a second signal having a second frequency, the second signal electrostatically driving the MEMS resonator device at approximately a mechanical resonance frequency, causing mechanical vibration of the MEMS resonator device; a signal divider configured to divide the first signal into a probe signal and a local oscillator (LO) signal, the probe signal being applied to the MEMS resonator device and reflected by a capacitance of the MEMS resonator device to provide a reflected probe signal, wherein a reflection coefficient is modulated onto the reflected probe signal at the mechanical resonance frequency by variations in the capacitance induced by the mechanical vibration of the MEMS resonator device; and a mixer configured to mix the reflected probe signal and the LO signal and to output an intermediate frequency (IF) signal, the IF signal representing modulation of the reflection coefficient, providing an image of the mechanical vibration of the MEMS resonator device.
 2. The system of claim 1, further comprising: a receiver configured to receive the IF signal for analysis of changes in amplitude and phase of the IF signal.
 3. The system of claim 2, wherein the receiver comprises one of a lock-in amplifier, a spectrum analyzer or a vector network analyzer.
 4. The system of claim 1, further comprising: a phase shifter configured to phase shift the LO signal in order to optimize operation of the frequency mixer.
 5. The system of claim 1, wherein the first frequency is a microwave frequency.
 6. The system of claim 1, wherein the signal divider comprises a directive coupler or a resistive divider.
 7. A system for detecting microscopic particles in an atomic force microscopy (AFM) application, the system comprising: a first signal source configured to provide a probe signal to a micro-electromechanical system (MEMS) resonator device via a first signal path, the probe signal being reflected by a capacitance of the MEMS resonator device to provide a reflected probe signal modulated by a reflection coefficient; a second signal source configured to provide a stimulus signal to the MEMS resonator device via a second signal path, the stimulus signal electrostatically driving the MEMS resonator device at about a mechanical resonance frequency, causing mechanical vibration of the MEMS resonator device, wherein the reflection coefficient is modulated on the reflected probe signal by variations in the capacitance induced by the mechanical vibration of the MEMS resonator device; and a mixer configured to mix the reflected probe signal and a local oscillator (LO) signal, having an LO frequency equal to a frequency of the probe signal, to demodulate the reflected, probe signal and to output an intermediate frequency (IF) signal, wherein the IF signal includes the reflection coefficient for providing an image of the mechanical vibration of the MEMS resonator device.
 8. The system of claim 7, further comprising: a signal divider configured to receive a first signal from the first signal source, and to divide available power of the first signal soiree into the probe signal provided to the first signal path and the LO signal provided to an LO signal path.
 9. The system of claim 8, wherein the signal divider comprises one of a directive coupler or a resistive divider.
 10. The system of claim 8, wherein the LO signal path comprises: a phase shifter configured to adjust a delay of the LO signal from the signal divider; and a band-pass filter configured to remove at least one of added noise and spurious signals from the phase shifted LO signal, a center frequency of the band-pass filter being substantially the same as a center frequency of the first signal.
 11. The system of claim 7, wherein the first signal path comprises: a high-pass filter for filtering the probe signal; and a first bias-tee for applying DC bias to the filtered probe signal.
 12. The system of claim 11, wherein the second signal path comprises: a second bias-tee for applying DC bias to the stimulus signal; and a low-pass filter for filtering the DC-biased stimulus signal.
 13. The system of claim 7, further comprising: a receiver configured, to receive the IT signal from the mixer via an IF signal path to be analyzed in terms of at least one of magnitude and phase.
 14. The system of claim 13, wherein the IF signal path comprises: a block capacitor configured to suppress a DC component of the IF signal; at least one amplifier configured to amplify the IF signal; and a low-pass filter configured to eliminate undesirable high frequencies components.
 15. A method for detecting responses of a micro-electromechanical system (MEMS) resonator device, the method comprising: applying a stimulus signal to a first transducer of the MEMS resonator device to induce mechanical vibration; applying a probe signal to a second transducer of the MEMS resonator device; receiving a reflected probe signal from the second transducer of the MEMS resonator device, the reflected probe signal having a reflection coefficient modulated onto the reflected probe signal at a resonance frequency of the MEMS resonator device by variations in a capacitance of the second transducer induced by the mechanical vibration of the MEMS resonator device; and demodulating the reflected probe signal with a local oscillator (LO) signal to obtain an intermediate frequency (IF) signal, providing an image of mechanical vibration, the LO signal having the same frequency as the probe signal.
 16. The method of claim 15, further comprising: determining characteristics of the MEMS resonator device using the IF signal.
 17. The method of claim 15, further comprising: adjusting a delay of the LO signal so that the LO signal and the reflected probe signal are in phase or 180 degrees out of phase.
 18. The method of claim 17, further comprising: dividing a microwave signal into the probe signal and the LO signal. 